Influence of nonholonomic constraints on variations, symplectic structure, and dynamics of mechanical systems

Abstract

Based on a serious analysis of the Frobenius integrability condition for affine differential constraints that mechanical systems are subject to the necessary and sufficient conditions for coincidence of three kinds of unfree variations, the existence of simple symplectic structure of the constraint submanifold and equivalence of nonholonomic and vakonomic dynamics for the constrained systems are, respectively, obtained, which are all related with the Frobenius integrability condition in their special forms. Two illustrative examples are presented to verify the results. © 2007 American Institute of Physics.